Boolean Intersect/Difference Only Uses Edges
Wow, I really don't know what I'm doing, huh?

Following a comment on the same YouTube video of the tutorial, I removed doubles.
(In Blender 2.80, it is now named "Merge by Distance, and can be found in Edit Mode, Mesh > Clean Up > Merge by Distance" 

So I learned a thing. I apologize if I wasted anyone's time with this.

\o/